Journal
NEW JOURNAL OF PHYSICS
Volume 20, Issue -, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1367-2630/aacde1
Keywords
orbital-free density-functional theory; degenerate fermion systems; semiclassical methods; split-operator approximation; gradient expansion; high-order leapfrog
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Funding
- Graduate School for Integrative Sciences & Engineering at the National University of Singapore
- Singapore Ministry of Education
- National Research Foundation of Singapore
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We improve on the Thomas-Fermi approximation for the single-particle density of fermions by introducing inhomogeneity corrections. Rather than invoking a gradient expansion, we relate the density to the unitary evolution operator for the given effective potential energy and approximate this operator by a Suzuki-Trotter factorization. This yields a hierarchy of approximations, one for each approximate factorization. For the purpose of a first benchmarking, we examine the approximate densities for a few cases with known exact densities and observe a very satisfactory, and encouraging, performance. As a bonus, we also obtain a simple fourth-order leapfrog algorithm for the symplectic integration of classical equations of motion.
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